Question

Find the value of "k" such that 1/2 is a root of 2x^2+11x=-k

Answer 1

The value of k is -6

Step-by-step explanation:

The general form of the quadratic equation is y = ax² + bx + c

• The roots of the equation is the values of x when y = 0
• ax² + bx + c = 0, is used to find the roots

∵ 2x² + 11x = -k

- Add k to both sides

∴ 2x² + 11x + k = 0

∵ The roots of the quadratic equations is the values of x when y = 0

∵ $\frac{1}{2}$ is a root of the equation

- Substitute x by $\frac{1}{2}$ in the equation above to find k

∵ 2( $\frac{1}{2}$ )² + 11( $\frac{1}{2}$ ) + k = 0

∴ 2( $\frac{1}{4}$ ) + $\frac{11}{2}$ + k = 0

∴ $\frac{1}{2}$ + $\frac{11}{2}$ + k = 0

- Add the like terms

∵ $\frac{1}{2}$ + $\frac{11}{2}$ = $\frac{12}{2}$ = 6

∴ 6 + k = 0

- Subtract 6 from both sides

∴ k = -6

The value of k is -6

Learn more:

You can learn more about the quadratic equations in brainly.com/question/8196933

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